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Localised Gravity and Resolved Braneworlds
High Energy Physics - Theory · Submitted 7 Nov 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Localising gravity about braneworld spacetimes requires finding solutions to transverse-space self-adjoint Sturm-Liouville problems admitting a normalisable zero mode in the noncompact transverse space.
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Deriving an effective massless field theory for fluctuations about a braneworld spacetime requires analysis of the transverse-space-wavefunction's second-order differential equation. There can be two strikingly different types of effective theory. For a supersymmetric braneworld, one involves a technically consistent embedding of a supergravity theory on the worldvolume; the other can produce, in certain situations, a genuine localisation of gravity near the worldvolume but not via a technically consistent embedding. So, in the latter situation, the theory's dynamics remains higher-dimensional but there can still be a lower-dimensional effective-theory interpretation of the dynamics at low worldvolume momenta / large worldvolume distances. This paper examines the conditions for such a gravity localisation to be possible. Localising gravity about braneworld spacetimes requires finding solutions to transverse-space self-adjoint Sturm-Liouville problems admitting a normalisable zero mode in the noncompact transverse space. This in turn requires analysis of Sturm-Liouville problems with radial singular endpoints following a formalism originating in the work of Hermann Weyl. Examples of such gravity-localising braneworld systems are found and analysed in this formalism with underlying "skeleton" braneworlds of Salam-Sezgin, resolved D3-brane and Randall-Sundrum II types.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Deriving an effective massless field theory for fluctuations about a braneworld spacetime requires analysis of the transverse-space-wavefunction's second-order differential equation. | background 0.93 | 0.12 | 0.04 | asserted 1.00 |
| s1 | There can be two strikingly different types of effective theory. | background 0.67 | 0.10 | 0.04 | hedged possibility 0.52 |
| s2 | For a supersymmetric braneworld, one involves a technically consistent embedding of a supergravity theory on the worldvolume; the other can produce, in certain situations, a genuine localisation of gravity near the worldvolume but not via a technically consistent embedding. | background 0.84 | 0.14 | 0.10 | hedged possibility 0.62 |
| s3 | So, in the latter situation, the theory's dynamics remains higher-dimensional but there can still be a lower-dimensional effective-theory interpretation of the dynamics at low worldvolume momenta / large worldvolume distances. | interpretation 0.86 | 0.14 | 0.09 | hedged possibility 0.93 |
| s4 | This paper examines the conditions for such a gravity localisation to be possible. | contribution 0.97 | 0.56 | 0.07 | asserted 0.81 |
| s5 | Localising gravity about braneworld spacetimes requires finding solutions to transverse-space self-adjoint Sturm-Liouville problems admitting a normalisable zero mode in the noncompact transverse space. | method 0.56 | 0.15 | 0.15 | asserted 1.00 |
| s6 | This in turn requires analysis of Sturm-Liouville problems with radial singular endpoints following a formalism originating in the work of Hermann Weyl. | method 0.82 | 0.17 | 0.04 | asserted 1.00 |
| s7 | Examples of such gravity-localising braneworld systems are found and analysed in this formalism with underlying "skeleton" braneworlds of Salam-Sezgin, resolved D3-brane and Randall-Sundrum II types. | contribution 0.70 | 0.91 | 0.12 | asserted 1.00 |
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The paper
Original abstract
Deriving an effective massless field theory for fluctuations about a braneworld spacetime requires analysis of the transverse-space-wavefunction's second-order differential equation. There can be two strikingly different types of effective theory. For a supersymmetric braneworld, one involves a technically consistent embedding of a supergravity theory on the worldvolume; the other can produce, in certain situations, a genuine localisation of gravity near the worldvolume but not via a technically consistent embedding. So, in the latter situation, the theory's dynamics remains higher-dimensional but there can still be a lower-dimensional effective-theory interpretation of the dynamics at low worldvolume momenta / large worldvolume distances. This paper examines the conditions for such a gravity localisation to be possible. Localising gravity about braneworld spacetimes requires finding solutions to transverse-space self-adjoint Sturm-Liouville problems admitting a normalisable zero mode in the noncompact transverse space. This in turn requires analysis of Sturm-Liouville problems with radial singular endpoints following a formalism originating in the work of Hermann Weyl. Examples of such gravity-localising braneworld systems are found and analysed in this formalism with underlying "skeleton" braneworlds of Salam-Sezgin, resolved D3-brane and Randall-Sundrum II types.
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What this paper does with the arXiv papers it cites
What it cites · 36 sentences without a confident label
Uses the method or tool of 2 papers
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Consider a transverse-traceless perturbation of the Minkowski worldvolume that depends both on the worldvolume coordinates as well as the Eguchi-Hanson radius $ρ$, [equation] From the general results of [ref] , the equations of motion to first-order in perturbations are satisfied provided that [equation] where $_4$ and $_EH$ are the respectively the Laplacians on $R^1,3$ and Eguchi-Hanson space.
Spin-2 spectrum of defect theories · Resolved D3-branes on Eguchi-Hanson space: consistently embedded worldvolume supergravity versus genuine localisations · 0.83
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To obtain such a solution, we will follow the recipe of [ref] and propose the ansatz[In the language of [ref] , we have $Ĝ_(3) = L_(3)$, where $L_(3)$ is a complex self-dual three-form satisfying $∗_6L_(3) = iL_(3)$, where $∗_6$ is the Hodge dual with respect to the Ricci-flat metric on $M_4×T^2$.] [equation] Here, $_4$ is the volume form on $R^1,3$, $z$ is the complex coordinate on $T^2$, the Ricci-flat metric on the Eguchi-Hanson space is [equation] with $ρ≥0$, $χ∈[0,2π)$, $θ∈[0,π]$ and $φ∈[0,2π)$; $∗_EH$ is the Hodge dual with respect to $ds^2_EH$, $H$ is a function on the Eguchi-Hanson space, and $F_(2)$ is the unique (up to normalisation), self-dual harmonic two-form on the Eguchi-Hanson space given by [equation] All of the equations of motion are satisfied provided that $H$ is a solution to the Poisson equation [equation] Assuming spherical symmetry, $H = H(ρ)$, the explicit soluti
Brane Resolution Through Transgression · Resolved D3-branes on Eguchi-Hanson space: consistently embedded worldvolume supergravity versus genuine localisations · 0.99
Uses data or values from 1 paper
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From [ref] , the requisite function $H$ is [equation] Defining $z = r-b ∈[0,∞)$, the relevant SLP is then [equation] which can be put into the form of [ref] with $p(z) = z^2$ and $μ(z) = z$.
Brane Resolution Through Transgression · Example 6 (no localisation): NS5-branes on Taub-NUT · 0.94
Compares with 2 papers
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Compared to the Salam-Sezgin solution of Type IIA supergravity, which can be interpreted as a resolved NS5-brane with $B$ being Eguchi-Hanson space, we find that the metric in [ref] lacks a fibration of one of the worldvolume coordinates over $B$ (see [ref] ).
Braneworld localisation in hyperbolic spacetime · Localised worldvolume gravitons on resolved branes · 0.98
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Our solution [ref] is a cousin of the Type IIA solution of [ref] which describes the ten-dimensional embedding of the $R^1,3×S^2$ Salam-Sezgin vacuum with an NS5-brane inclusion, where the NS5-brane has a tension proportional to the parameter $k$.
A String and M-theory Origin for the Salam-Sezgin Model · Resolved D3-branes on Eguchi-Hanson space: consistently embedded worldvolume supergravity versus genuine localisations · 0.98
Cites as support 2 papers
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As shown in [ref] , the gauge symmetry is preserved due to the existence of a field with a Stueckelberg-like transformation that only appears when we consider the full, ten-dimensional gravity perturbation $ĝ_MN ↦ĝ_MN + Ĥ_MN$, and not just the worldvolume, transverse-traceless part.
Covert Symmetry Breaking · Resolved D3-branes on Eguchi-Hanson space: consistently embedded worldvolume supergravity versus genuine localisations · 1.00
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This Stueckelberg-like field was shown in [ref] to be a phantom mode – it only contributes to the energy of the effective field theory at interacting level.
Higgs Effect Without Lunch · Resolved D3-branes on Eguchi-Hanson space: consistently embedded worldvolume supergravity versus genuine localisations · 0.99
Cites as background 9 papers
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Consideration of source terms have been treated in Ref. [ref] and also more recently in Ref. [ref] .]
Harmonic functions and gravity localization · Introduction: Brane dynamics taxonomy · 0.83
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Consideration of source terms have been treated in Ref. [ref] and also more recently in Ref. [ref] .]
Braneworld localisation in hyperbolic spacetime · Introduction: Brane dynamics taxonomy · 0.83
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Such effective theories of massless modes supported by non-constant zero eigenfunctions were studied in [ref] .
Higgs Effect Without Lunch · Resolved D3-branes on Eguchi-Hanson space: consistently embedded worldvolume supergravity versus genuine localisations · 0.80
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